Indefinite-Metric Quantum Field Theory

Abstract

Some recent progress in the quantum field theory based on the indefinite-metric Hilbert space is reviewed in a systematic way. Various problems (as shown in the table of contents below) are discussed extensively. The selection of topics is, however, dependent on the present author's interest; undescribed topics do not necessarily mean to be unimportant. An almost complete exposition is given concerning the finite-dimensional indefinite-metric space. On the indefinite-metric quantum field theory, the problem of interpretation and the unitarity of the physical S-matrix are discussed in detail. Also included are a number of new results and remarks on various existing theories. Some of them are construction of a field theory having only one Feynman integral, critical remarks on the quantization of a purely-imaginary-mass field and a criticism of the renormalization procedure of the Gupta-Bleuler quantum electrodynamics.